Hardware-Free Polarization Stabilization for Measurement-Device-Independent Quantum Key Distribution via Correlated Twirling

Abstract: Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) provides unconditional security against detector vulnerabilities, but its practical deployment is severely hindered by asymmetric channel turbulence. Fluctuations in optical fibers induce arbitrary polarization drift, degrading Hong-Ou-Mandel interference and forcing extensive calibration downtime. In this work, we propose a hardware-free polarization stabilization technique utilizing a Correlated Twirling protocol based on a unitary 2-design. By applying a synchronized, public twirling supermap, Alice and Bob mathematically transform deterministic, asymmetric geometric rotations into an isotropic Pauli depolarizing channel. Executed entirely as a virtual post-processing step during classical sifting, this protocol mathematically suppresses intrinsic channel noise by a factor of 2/3. We demonstrate through exact quantum state simulations that this induced symmetry neutralizes catastrophic axis-dependent failures, extending the Y-bias tolerance from 0.68 to 0.84 radians. Furthermore, the protocol passively extends the absolute angular misalignment tolerance for the 11% security threshold from $38.7<sup>\circ$ to $47.9<sup>\circ$, sustaining secure key distillation over extended fiber distances in highly turbulent regimes where standard architectures fail. Inherently compatible with decoy-state weak coherent pulses, this algorithmic approach provides a highly scalable, resource-efficient framework for robust long-distance quantum networks.